100 bets in one day - kelly adjustment?
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GanchrowSBR Hall of Famer
- 08-28-05
- 5011
#36Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#37How is this a "real world" scenario precisely, BigCap? You're proposing a situation that is as likely as hitting the four Powerball numbers that you are railing against. It is certainly POSSIBLE to lose every bet no matter how slim the liklihood may be. AGAIN, there MUST be some bounds to the credit availability. And if there weren't, although I'm not quite certain how, you'd need a utility function that would be independent for each person's level of comfort with risk of ruin.
It is not possible in the real world to lose 100 bets as described, and there is no real point in discussing the possibility. I think we have moved on from that discussion.Comment -
GanchrowSBR Hall of Famer
- 08-28-05
- 5011
#38And actually, your original question was, ""How much should I bet on each assuming I want to maximize growth?"
The answer of course remains a tad less than $1,000 per bet.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#39Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#40Again, I think we have moved past considering losing all 100 bets as a possible real world outcome. This is why "a tad less than $1,000 per bet" is not the correct answer.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#41You are getting a bit closer to the answer. Betting on books' credit and clearing the books the next day is how the business was run for years. It is still being done this way for many books. Again, you are misconstruing books' credit with one obtaining credit against future net worth. The books providing you credit are not adding to your net worth or increasing your bankroll; they are only facilitating placing of wagers in a convenient way so you do not need to drive up to their location and drop the cash.
It is not possible in the real world to lose 100 bets as described, and there is no real point in discussing the possibility. I think we have moved on from that discussion.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#42Please provide the math which proves the assertion that losing 100 bets is not possible. Thanks.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#43
There is a correct answer, and it can be demonstrated. I am reasonably certain now that you and others here can now answer this question, once Kelly Criterion application is recognized as not providing the correct answer.Comment -
GanchrowSBR Hall of Famer
- 08-28-05
- 5011
#44We're running around in circles here.
But to be crystal clear, in answer to your initial question, "How much should I bet on each [of these 100 independent 3% edge even odds bets] assuming I want to maximize [bankroll] growth?"
The answer is a tad less than 1% of bankroll per bet.
I'd be more than happy to entertain and critique (and of course ultimately refute) any mathematical proof to the contrary. The same I'm sure would for Monkey.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#45Again, this is not possible in the real world. Any reasonable person should be able to recognize this. Let's move on from this pointless discussion as I am sure you would agree that you would never consider this possibility in any of your future planning. It really is nonsense.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#46We're running around in circles here.
But to be crystal clear, in answer to your initial question, "How much should I bet on each [of these 100 independent 3% edge even odds bets] assuming I want to maximize [bankroll] growth?"
The answer is a tad less than 1% of bankroll per bet.
I'd be more than happy to entertain and critique (and of course ultimately refute) any mathematical proof to the contrary.
If you do consider losing 100 bets as described a real world possibility, then you are not being reasonable as no reasonable person would ever consider this a real world possibility. So either choice is incorrect.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#47Again, this is not possible in the real world. Any reasonable person should be able to recognize this. Let's move on from this pointless discussion as I am sure you would agree that you would never consider this possibility in any of your future planning. It really is nonsense.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#48
I am certain you agree this event will never happen in your lifetime, which is sufficient to conclude it will not happen for your planning. Any disagreement to this is just being disingenuous.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#49That's absurd. You can't maximize growth by ignoring possible outcomes.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#50
Anything otherwise is not reasonable.
No one would ever consider this outcome in this situation.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#51Please provide the math which proves otherwise.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#52Are you being unreasonable, i.e. considering the possibility of losing 100 consecutive 51.5% bets? This is my only explanation to why you have posed this question. I already answered this, in that no logical, reasonable person would ever consider this a possibility in their planning. I know for certain that you would never consider this in your planning, i.e. if you were in the situation I posed above. I am certain you would bet more than 1% of your bankroll because you would want to maximize growth. Considering losing 100 consecutive bets would be absurd. You may post otherwise, but I would appreciate some honesty in this case.
This is a perfect assumption that will never fail for this example. You are trying to apply theory for a practical situation in which the theory does not apply (e.g. Kelly).Comment -
GanchrowSBR Hall of Famer
- 08-28-05
- 5011
#53Simple mathematical proof as to why bet size need be less than 1% of bankroll in order to maximize bankroll growth:
Expected bankroll growth would in this case be defined as:QED
Now if we allow x = 1%, then the 1st term of the summation (i=0) reduces to:(1+(2*0-100)*.01)combin(100,0)*0.5150*0.485100As the product of any given set of finite numbers that includes zero equals zero then our E(growth) equals:
=01*1*0.485100
=0
0 - 1In other words a bet size = 1% would imply -100% expected bankroll "growth", (which in full Kelly terms equates to -∞ utility).
= -100%
Hence, bet size must be < 1%.
Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#54Simple mathematical proof as to why bet size need be less than 1% of bankroll in order to maximize bankroll growth:Expected bankroll growth would in this case be defined as:
Now if we allow x = 1%, then the 1st term of the summation (i=0) reduces to:(1+(2*0-100)*.01)combin(100,0)*0.5150*0.485100As the product of any given set of finite numbers that includes zero equals zero then our E(growth) equals:
=01*1*0.485100
=0
0 - 1In other words a bet size = 1% would imply -100% expected bankroll "growth", (which in full Kelly terms equates to -∞ utility).
= -100%
Hence, bet size must be < 1%.
QED
Again, this theory does not apply because of the reasons noted.
I would appreciate an honest answer to the question posed, WITHOUT THEORY. Just put yourself in the player's shoes and make a logical choice on how much you would bet. I know what the theory produces, and I know why I can logically dismiss it.Comment -
GanchrowSBR Hall of Famer
- 08-28-05
- 5011
#55Again, either you are considering losing 100 consecutive bets as a real world possibility (which is not reasonable), or you are not being honest with your intention of betting more than 1% in this case.
Again, this theory does not apply because of the reasons noted.
I would appreciate an honest answer to the question posed, WITHOUT THEORY. Just put yourself in the player's shoes and make a logical choice on how much you would bet. I know what the theory produces, and I know why I can logically dismiss it.
We're talking about maximizing expected bankroll growth, which is a rather straightforward mathematical concept.
Perhaps your own personal bankroll management goals do not encompass the maximization of bankroll growth. That's fine by me, and certainly in no normative manner is either "better" or "worse" than a set of goals that does.
But go ahead ... argue how that's not how you'd personally behave if faced with such a scenario and you won't hear a peep out of me. Such is simply a matter of personal preferences and I have no more right to dictate yours when it comes to bankroll management than I have when it comes to your choice between flavors of ice cream or methodology for consuming Oreo cookies.
BUT:
That was NOT your original question. YOU asked about the maximization of bankroll growth and I (and Monkey) responded with the correct answer. Whether YOU like it or not, whether YOU would behave this way or not, whether it ultimately angers YOU to no end or not, that the maximization of expected bankroll growth necessitates betting less than 1% of bankroll per wager remains an immutable mathematical fact that I easily proved in post #53 of this thread.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#56Not sure what more I can say.
We're talking about maximizing expected bankroll growth, which is a rather straightforward mathematical concept.
Perhaps your own personal bankroll management goals do not encompass the maximization of bankroll growth. That's fine by me, and certainly in no way normative manner either "better" or "worse" than a set of goals that do.
So go ahead ... argue how that's not how you'd personally behave if faced with such a scenario and you won't hear a peep out of me. Such is simply a matter of personal preferences and I have no more right to dictate yours when it comes to bankroll management than I have when it comes to your choice between flavors of ice cream or methodology for consuming Oreo cookies.
BUT:
That was NOT your original question. YOU asked about the maximization of bankroll growth and I (and Monkey) responded with the correct answer. Whether YOU like it or not, whether YOU would behave this way or not, and no matter how much it might anger YOU, that the maximization of expected bankroll growth necessitates betting less than 1% of bankroll per wager remains an immutable mathematical fact.
Losing 100 events as described will NOT HAPPEN IN THE REAL WORLD. This is why the theory cannot be applied. I am not going to beat an apparent dead horse here with trying to obtain your non-theoretical answer to this question. Again, I am certain you would always rule out losing 100 of these bets in your planning. You never disputed this so I can only conclude it true. As such you would always bet (correctly) at more than 1%. I believe this a logical conclusion as you never provided an honest answer in this way.
Either you recognize this event will never happen (and construct an appropriate model for the solution), or you don't want to admit such (and thus are unreasonable).Last edited by BigCap; 06-15-09, 04:54 PM.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#57AGAIN, any wagers of 1% or greater come down to personal utility. If you had proposed a realistic situation, then perhaps your argument of a "real world" approach could hold some weight. But you haven't and it doesn't. What remains is that your idea of bankroll is misconstrued and that if this scenario were ever encountered in the "real world," anyone wishing to exceed their bankroll would need to factor in their own utility in determining how much risk of ruin they wish to take on. There is no denying there is risk there, no matter how small it may be. That amount of risk also increases exponentially the more possible outcomes that person is willing to write off.Comment -
RickySteveRestricted User
- 01-31-06
- 3415
#58Pretty much the best thread ever.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#59Correct, which led me to believe you were on the right course. But anything less than 1% is not logically correct under any reasonable cirrcumstances.
What remains is that your idea of bankroll is misconstrued and that if this scenario were ever encountered in the "real world," anyone wishing to exceed their bankroll would need to factor in their own utility in determining how much risk of ruin they wish to take on. There is no denying there is risk there, no matter how small it may be. That amount of risk also increases exponentially the more possible outcomes that person is willing to write off.
Let me pose another example, which you will probably post a rejection either because (a) it is not "real world" (but your attempted application of theory to this problem is not real world at all), or (b) proves your approach to be in error (which I am reasonably certain you would not admit to anyway). It has no logical answer other than a confirmation that I am correct:
Portfolio manager: Joe, I have some potential investment opportunities that will increase your portfolio by 25% each year over the next 10 years.
Joe: Sounds good, but what is the risk?
Portfolio manager: Well, we modeled this investment and the only risk we came up with is a 10E-500 chance of losing everything.
Joe: Everything?
Portfolio manager: Yes, everything you own, or ever could own would be gone. Your effective net worth would be zero.
Joe: Can you give me an example of what 10E-500 chance would be?
Portfolio manager: Sure. It would be about the same chance that you would play one ticket each week on powerball, win this week, then win next week, and so on for the next 80 weeks.
Joe: I think I can live with that. That is never going to happen, so why worry about it?
Portfolio manager: Exactly, it will never happen.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#60This is laughable. Seriously. If you ONLY exclude the 0 wins combination out of your risk calculation, guess what? Your optimal wager will still be very close to 1% of your bankroll. And really? That's the ONLY risk here? Please. What if you're extending your bankroll to wager $200k on these events with this credit and go 29-67-4? Is that within the "real world" possibilities maybe? What have you stated in regards to utilizing the credit as a portion of your bankroll? It is indisputable that it would now be considered a portion of your bankroll. What else is it? You can't extend your bankroll without that money being considered a part of it. And NO IT ISN'T REALISTIC. I've never heard of a book that offered credit with infinite limits. Certainly, such a book DOES NOT EXIST. If there were such a book, why not just Martingale all day long? Not only that, but this book also will not offer parlays? Please don't tell me this is due to risk aversion. LOL. You're in outer space on this one. This isn't a black and white question, and it's certainly not realistic.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#61And by the way, what we're proposing is close to a zero net worth possibility at 3.75E-32. What you're proposing is a negative net worth at far better odds.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#62
I'm sure you are aware that book (A) will not be so kind to offer you a parlay a bet with the same odds as book (B), each of which offer the favorable odds. And I'm in outer space? Wow, get a clue, really. You are clearly wrong on each and every point.Last edited by BigCap; 06-15-09, 09:23 PM.Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#63
Other than the above figure you have been 100% wrong. You are clearly reaching on this, trying to distort my initial question with pointless exaggerations and untruths. Every point you have attempted has been easily refuted. You already acknowledged you were wrong about the < 1% figure. At this point I would save some grace because it will not get any better for you on this one.
Enough said.Last edited by BigCap; 06-15-09, 09:31 PM.Comment -
DazzezSBR Sharp
- 08-04-06
- 258
#64So hey BigCap. Are you saying that Ganchrow, Monkeyfocker and Kelly are all wrong when they say that to maximize BR growth you should bet less than 1% of BR per bet?Comment -
BigCapSBR High Roller
- 02-10-08
- 189
#65
Kelly applied to this question is incorrect, as I have shown. So it should not be included in the above group. And Monkey... already admitted as such that > 1% is correct.Comment -
DazzezSBR Sharp
- 08-04-06
- 258
#66
And anyway you haven't show sh*t. You gave a little qualitative argument with no matematcial reasoning for why you believe what you do but still obviously haven't didn't read that Ganch post linked on how to properly measure a bankroll, or his proof decimates your argument completely.
So if you think ganch amd monkey are both wrong then wheres your mathematical reasoning? Or are you one of those people who "don't believe that math always tells the whole story" or some other such drivel?Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#67
And what exactly is your point here? That with $100k bankroll my position is correct, but with $200k it is not? This is laughable.
Again, we do not need to dwell on this further. My bet ratio to my bankroll for a single bet would not change one bit if I had the convenience of placing my bets with a book and clearing them the next day. I think you should be able to rationalize this by now. Get serious.
Who on earth is talking about "infinite limits"? You are way off base here.Last edited by MonkeyF0cker; 06-15-09, 10:56 PM.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#68Originally posted by BigCap
Books still exist that offer the convenience of clearing the next day. You cannot be this ignorant. Sure, Martingale and see what happens to your knee caps when tomorrow comes and you can't pay. Maybe somebody will go further and find a nice hole in the desert.
I'm sure you are aware that book (A) will not be so kind to offer you a parlay a bet with the same odds as book (B), each of which offer the favorable odds. And I'm in outer space? Wow, get a clue, really. You are clearly wrong on each and every point.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#69Look. We've asked multiple times for you to provide mathematical proof to your assertions. Until you do, everything you've said is nonsense. The onus is on you here. The Kelly Criterion has been time tested.Comment -
MonkeyF0ckerSBR Posting Legend
- 06-12-07
- 12144
#70At least you got 3.75E-32 right, which is a bit of a surprise. It does not change the fact that the event won't happen, and should not be considered in any future planning.
Other than the above figure you have been 100% wrong. You are clearly reaching on this, trying to distort my initial question with pointless exaggerations and untruths. Every point you have attempted has been easily refuted. You already acknowledged you were wrong about the < 1% figure. At this point I would save some grace because it will not get any better for you on this one.
Enough said.Last edited by MonkeyF0cker; 06-15-09, 11:28 PM.Comment
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